|2x + 5| = 3x + 4
I got x = 1 and x = -9/5 and neither of those work. Is it possible to have no solutions?

Question

|2x + 5| = 3x + 4
I got x = 1 and x = -9/5 and neither of those work. Is it possible to have no solutions?

anonymous · Answer

$x=1$ should definitely work. 

Plugging in $x=-\dfrac{9}{5}$, you have
$$\left|2\left(-\dfrac{9}{5}\right)+5\right|=3\left(-\dfrac{9}{5}\right)+4\
|\cdots|=-\frac{27}{5}+\frac{20}{5}\
|\cdots|=-\frac{7}{5}$$
Do you see why it doesn't work? Whenever you take the absolute value of something, you will never get a negative number.

anonymous · Answer

Oh gosh I wrote the wrong thing on my paper! xD Sorry thanks for pointing that out. I had a 4 instead of a 2 written down on accident. Thanks again!

anonymous · Answer

You're welcome!